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diff --git a/tests/testthat/test_saem.R b/tests/testthat/test_saem.R
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+context("Nonlinear mixed effects models fitted with SAEM from saemix")
+
+set.seed(123456)
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+n <- n_biphasic <- 15
+log_sd <- 0.3
+err_1 = list(const = 1, prop = 0.05)
+tc <- function(value) sigma_twocomp(value, err_1$const, err_1$prop)
+const <- function(value) 2
+
+SFO <- mkinmod(parent = mkinsub("SFO"))
+k_parent = rlnorm(n, log(0.03), log_sd)
+ds_sfo <- lapply(1:n, function(i) {
+  ds_mean <- mkinpredict(SFO, c(k_parent = k_parent[i]),
+    c(parent = 100), sampling_times)
+  add_err(ds_mean, tc, n = 1)[[1]]
+})
+
+DFOP <- mkinmod(parent = mkinsub("DFOP"))
+dfop_pop <- list(parent_0 = 100, k1 = 0.06, k2 = 0.015, g = 0.4)
+dfop_parms <- as.matrix(data.frame(
+  k1 = rlnorm(n, log(dfop_pop$k1), log_sd),
+  k2 = rlnorm(n, log(dfop_pop$k2), log_sd),
+  g = plogis(rnorm(n, qlogis(dfop_pop$g), log_sd))))
+ds_dfop <- lapply(1:n, function(i) {
+  ds_mean <- mkinpredict(DFOP, dfop_parms[i, ],
+    c(parent = dfop_pop$parent_0), sampling_times)
+  add_err(ds_mean, const, n = 1)[[1]]
+})
+
+set.seed(123456)
+DFOP_SFO <- mkinmod(
+  parent = mkinsub("DFOP", "m1"),
+  m1 = mkinsub("SFO"),
+  quiet = TRUE)
+syn_biphasic_parms <- as.matrix(data.frame(
+  k1 = rlnorm(n_biphasic, log(0.05), log_sd),
+  k2 = rlnorm(n_biphasic, log(0.01), log_sd),
+  g = plogis(rnorm(n_biphasic, 0, log_sd)),
+  f_parent_to_m1 = plogis(rnorm(n_biphasic, 0, log_sd)),
+  k_m1 = rlnorm(n_biphasic, log(0.002), log_sd)))
+ds_biphasic_mean <- lapply(1:n_biphasic,
+  function(i) {
+    mkinpredict(DFOP_SFO, syn_biphasic_parms[i, ],
+      c(parent = 100, m1 = 0), sampling_times)
+  }
+)
+ds_biphasic <- lapply(ds_biphasic_mean, function(ds) {
+  add_err(ds,
+    sdfunc = function(value) sqrt(err_1$const^2 + value^2 * err_1$prop^2),
+    n = 1, secondary = "m1")[[1]]
+})
+
+test_that("Parent only models can be fitted with saemix", {
+  # Some fits were done in the setup script
+  mmkin_sfo_2 <- mmkin("SFO", ds_sfo, fixed_initials = c(parent = 100), quiet = TRUE)
+
+  sfo_saemix_2 <- saem(mmkin_sfo_1, quiet = TRUE, transformations = "mkin")
+  sfo_saemix_3 <- expect_error(saem(mmkin_sfo_2, quiet = TRUE), "at least two parameters")
+  s_sfo_s1 <- summary(sfo_saemix_1)
+  s_sfo_s2 <- summary(sfo_saemix_2)
+
+  sfo_nlme_1 <- expect_warning(nlme(mmkin_sfo_1), "not converge")
+  s_sfo_n <- summary(sfo_nlme_1)
+
+  # Compare with input
+  expect_equal(round(s_sfo_s2$confint_ranef["SD.log_k_parent", "est."], 1), 0.3)
+  # k_parent is a bit different from input 0.03 here
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3), 0.035)
+  expect_equal(round(s_sfo_s2$confint_back["k_parent", "est."], 3), 0.035)
+
+  # But the result is pretty unanimous between methods
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
+    round(s_sfo_s2$confint_back["k_parent", "est."], 3))
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
+    round(s_sfo_n$confint_back["k_parent", "est."], 3))
+
+  mmkin_dfop_1 <- mmkin("DFOP", ds_dfop, quiet = TRUE)
+
+  dfop_saemix_1 <- saem(mmkin_dfop_1, quiet = TRUE, transformations = "mkin")
+  dfop_saemix_2 <- saem(mmkin_dfop_1, quiet = TRUE, transformations = "saemix")
+  dfop_nlme_1 <- nlme(mmkin_dfop_1)
+  s_dfop_s1 <- summary(dfop_saemix_1)
+  s_dfop_s2 <- summary(dfop_saemix_2)
+  s_dfop_n <- summary(dfop_nlme_1)
+
+  dfop_pop <- as.numeric(dfop_pop)
+  expect_true(all(s_dfop_s1$confint_back[, "lower"] < dfop_pop))
+  expect_true(all(s_dfop_s1$confint_back[, "upper"] > dfop_pop))
+  expect_true(all(s_dfop_s2$confint_back[, "lower"] < dfop_pop))
+  expect_true(all(s_dfop_s2$confint_back[, "upper"] > dfop_pop))
+
+
+  # We get < 20% deviations with transformations made in mkin
+  rel_diff_1 <- (s_dfop_s1$confint_back[, "est."] - dfop_pop) / dfop_pop
+  expect_true(all(rel_diff_1 < 0.2))
+
+  # We get < 8% deviations with transformations made in saemix
+  rel_diff_2 <- (s_dfop_s2$confint_back[, "est."] - dfop_pop) / dfop_pop
+  expect_true(all(rel_diff_2 < 0.08))
+})
+
+test_that("Simple models with metabolite can be fitted with saemix", {
+
+  dfop_sfo_pop <- as.numeric(dfop_sfo_pop)
+  ci_dfop_sfo_s_s <- summary(saem_biphasic_s)$confint_back
+  expect_true(all(ci_dfop_sfo_s_s[, "lower"] < dfop_sfo_pop))
+  expect_true(all(ci_dfop_sfo_s_s[, "upper"] > dfop_sfo_pop))
+
+  # The following does not work, the k1 and k2 are not fitted well
+  ci_dfop_sfo_s_m <- summary(saem_biphasic_m)$confint_back
+  # expect_true(all(ci_dfop_sfo_s_m[, "lower"] < dfop_sfo_pop))
+  #expect_true(all(ci_dfop_sfo_s_m[, "upper"] > dfop_sfo_pop))
+
+  # Somehow this does not work at the moment. But it took forever (~ 10 min) anyways...
+  #saem_biphasic_2 <- saem(mmkin_biphasic, solution_type = "deSolve", quiet = TRUE)
+
+})